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1 vote
What is the complete factorization of the polynomial below?
x3 + 4x2 + 16x + 64

User Siv Rj
by
6.9k points

1 Answer

2 votes

Answer: (x+4) ( x-4i)(x+4i)

Discussion:

Factor the polynomial:

x^3+4x^2+16x+64 = (x +4 ) ( x^2 + 16) (*)

Factor x^2 +1 6 over the complex numbers:

x^2 + 16 = (x -4i)(x+4i) (**)

Combing (*) and (**) gives the full factorization

(x+4) ( x-4i)(x+4i)

User Nkitku
by
7.0k points
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